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Applying Perturbation Methods to Incomplete Market Models with Exogenous Borrowing Constraints

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  • Henry Kim
  • Jinill Kim
  • Robert Kollmann

Abstract

This paper solves an incomplete market model with infinite number of agents and exogenous borrowing constraints described in den Haan, Judd and Juillard (2004). We apply the idea of “barrier methods” to convert optimization problem with borrowing constraints as inequalities into a problem with equality constraints, and the converted model is solved by a second-order perturbation method. The simulation results of impulse responses and second moments match the standardized features of incomplete market models. Accuracy of the solution is in a reasonable range but significantly decreases when the economy is near the borrowing limit or moves away from the steady state.

Suggested Citation

  • Henry Kim & Jinill Kim & Robert Kollmann, 2005. "Applying Perturbation Methods to Incomplete Market Models with Exogenous Borrowing Constraints," Discussion Papers Series, Department of Economics, Tufts University 0504, Department of Economics, Tufts University.
    • Handle: RePEc:tuf:tuftec:0504
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    References listed on IDEAS

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    8. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
    9. Jinill Kim & Sunghyun Henry Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
    10. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and Using Second Order Accurate Solutions of Discrete Time," Levine's Bibliography 666156000000000284, UCLA Department of Economics.
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    Cited by:

    1. Bingbing Dong, 2014. "Asset Pricing and Monetary Policy," 2014 Meeting Papers 881, Society for Economic Dynamics.
    2. Darlene Chisholm & Margaret McMillan & George Norman, 2010. "Product differentiation and film-programming choice: do first-run movie theatres show the same films?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 34(2), pages 131-145, May.
    3. Ioannides, Yannis M. & Soetevent, Adriaan R., 2007. "Social networking and individual outcomes beyond the mean field case," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 369-390.
    4. Gilbert Metcalf & Jongsang Park, 2007. "A comment on the role of prices for excludable public goods," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 14(6), pages 685-698, December.
    5. Antoni Calvo-Armengol & Yannis M. Ioannides, 2005. "Social Networks in Labor Markets," Discussion Papers Series, Department of Economics, Tufts University 0517, Department of Economics, Tufts University.
    6. Mr. Mauro F Roca, 2009. "Search in the Labor Market under Imperfectly Insurable Income Risk," IMF Working Papers 2009/188, International Monetary Fund.
    7. Andrea Pescatori, 2007. "Incomplete markets and households’ exposure to interest rate and inflation risk: implications for the monetary policy maker," Working Papers (Old Series) 0709, Federal Reserve Bank of Cleveland.
    8. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    9. Kim, Sunghyun Henry & Kollmann, Robert & Kim, Jinill, 2010. "Solving the incomplete market model with aggregate uncertainty using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 50-58, January.
    10. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    11. Darlene C. Chisholm & George Norman, 2006. "When to Exit a Product: Evidence from the U. S. Motion-Picture Exhibition Market," American Economic Review, American Economic Association, vol. 96(2), pages 57-61, May.

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    More about this item

    Keywords

    perturbation; barrier method; borrowing constraint; incomplete market; accuracy.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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